i found a cheap thermostat on clearance at the store. i thought it was a mechanical one (since it had no display) but later i found it needed batteries to operate. i didn't read the package close enough to notice. not that it matters, but figured a mechanical one would be more forgiving of my experiments. it is a millivolt/24v AC heat only thermostat.
anyway, i ran the battery power thru the thermostat, to the relay. hooked the relay outputs to the battery and load. initially, i used (1) 6v battery to power the thermostat. it worked, and drew about .2a thru the thermostat when operating the relay. then i hooked it to the 24v series of batts. again, worked fine and drew about .04a. so, either configuration, it appears to pass about 1 watt thru it. i don't know how long it will work, but for now, it does.